Pipe A and Pipe B can fill a tank in 12 mins and 6 mins respectively, whereas pipe C can empty it completely in 5 mins B is opened to fill an empty tank After some time, A and C are also opened, after which it takes 15 min to fill the tank. How long was B open alone?

"x" is the volume of the tank. Q denotes the flow rate of each respective pipe.

Let $t$ be the amount of time pipe B was open by itself and say the tank can hold $x$ litres.

In the time pipe B was on alone, it fills the tank with $\frac{tx}{6}$ litres of water. When pipe A and pipe C are also turned on for 15 minutes, the pipes combined fill the tank with $15(\frac{x}{6} + \frac{x}{12} - \frac{x}{5})$ litres of water.

Since the tank is filled up in this time, we can form the equation
$$\frac{tx}{6} + 15(\frac{x}{6} + \frac{x}{12} - \frac{x}{5}) = x.$$